I know that isn’t a big deal in lots of places, but here the streets and sidewalks are a mess, we get three days off of school, and on Friday it’s snowing a bit again and I have about 60% attendance. And there’s another storm brewing, and looks likely to be a snow day on Monday. What to do?

I decided to scrap (again) my planned lesson writing exponential functions from tables. Instead, we talked about population growth, collapse, and the environment.

**Part 1:** This comic, by Stuart McMillen, is really awesome. Below is the abridged version, but you should check out the whole thing.

This sparked some great discussion. I stopped them after the researches left the island and asked what they thought would happen next. They pretty much all guessed that there would be more reindeer, but no one was even close to guessing the speed of the population’s growth. Not surprising.

Then, after they learned there were 1,350 reindeer after 13 years, I told them the researchers were going to come back again in 6 years, and asked them to guess how many reindeer there would be. Guesses were again low, for the most part — I think this reflects a natural human challenge in comprehending and predicting exponential growth. It’s hard to physically see and make estimates for exponential growth, and making those predictions exponentially is pretty high on the ladder of abstraction.

Anyway, then there are 6,000 reindeer, and I told them the researchers would come back again in three years, and asked how many reindeer they thought there would be. Now some kids showed a better understanding of exponential growth, and a few predicted that they would decrease because they were running out of food. Some great discussion — but again, no one predicted that almost the entire population would die off in three years. We talked a bit about the idea of carrying capacity. I threw this graph at them, but I think it’s a bit beyond their understanding of functions at the moment:

Check out this article for a more in-depth discussion of what happened to the reindeer.

**Part Two:** “Ok Mr. Kane what do these reindeer have to do with us?”

This is where the lesson became a bit more off-the-cuff, but I just read a book about Easter Island, and with the help of Google I told the story, as best as I understand it, of population collapse on Easter Island — this time focusing on the specific resources, in particular trees, that they used up, and the effect on the population. The Moai (statues) were a pretty good hook for this one, and kids were pretty interested in what happened to the people who built them.

**Part Three:** Then we made things serious. “What are some of the things that we could use up that could cause this to happen to us?”

Kids brainstormed things that we need to function in society. I showed them this graph

of the United States population over time, and a few different models for predicting its growth. We talked about the implications of each model, and what that meant for the resources we would need.

That was about where class ended for each group, although we went off on a few different tangents — one class brought up the World Population Clock, others had different questions they wanted answered. They all learned some things about the world, and made some important connections between the world and the math that we’re learning. Can’t do this every day, but I think they learned something from it, and we all enjoyed it.

howardat58They’ll soon be ready for predator – prey models.

Here is a nice descriptive link

http://www.bbc.co.uk/schools/gcsebitesize/science/edexcel_pre_2011/environment/populationsandpyramidsrev5.shtml

and a rather mathematical one, but around page 22 (!) it gets easier.

http://www.tiem.utk.edu/workshop06/talks/Whittle_discretetime.ppt

recombinantrecordsGlad that you could make use of my St Matthew Island comic!